Elliot and Faye invest $5000 each in different banks

Question

Elliot and Faye invest $5000 each in different banks. Elliot earns annual rate of interest 12% compounded monthly and Faye earns annual rate of interest 12% compounded quarterly. If after 6 months Elliot earns a total interest of E, and Faye earns a total interest of F, which of the following must be true?

A. E=F
B. E>F
C. E<F
D. E=$300
E. F=$300

A. E=F
B. E>F
C. E<F
D. E=$300
E. F=$300

generis · Accepted Answer

No need to calculate, if compound interest is familiar. (If not, see the rule below.

) Principal amounts, interest rates, and time are identical. E gets paid more times than F. E will be greater than F. The rule is: All else being equal (principal, interest rate, and time period), whoever gets paid "interest on interest" more frequently has the highest rate of return and highest future value over time. If more frequent installments = greater future value, then Elliott wins. Elliott gets paid compounding interest 12 times a year, or 6 times in 6 months. Faye gets paid compounding interest 4 times a year, or 2 times in six months. No matter what, over time, Elliott earns more "interest on interest." But if you sense that the difference is not huge (and it is not here - six months is too short a time), and you want to be sure . . . you can choose an easier principal amount and round a little. $10,000 at 12%? Choose a big principal. For rate, stay with 12 percent for ease of division. E gets .12/12 = .01 every month F gets .12/4 = .03 every 3 months Amount with interest added in, for months 1-6: E: 10100, 10201, 10303, 10406, 10510, 10615 F: 10000, 10000, 10300, 10300, 10300, 10,609 E > F ANSWER B Actual difference here is not huge. After six months: Elliott has $5,307.60 And Faye has $5,304.50 Still, E has about $3.00 more. That is all that matters. Over time, E will be greater than F by quite a bit.

laddaboy · Answer

Need to input numbers and solve.

Amount Elliot earns after 6 months is $5307.60 while Faye earns $5304.50. Interest earned by Elliot is greater than interest earned by Faye.

saswata4s · Answer

You can answer this without calculation.

If investment amount and interest rate is same, the amount which is compounded more frequently will be greater.

for same amount and interest rate, the total interest earned for 6 months will be:

compounded daily > compounded weekly > compounded monthly > compounded half-yearly

Ans: B.

ApplicantX · Answer

Interest rate for 6 months of E would be greater than interest rates for 6 months of F. 
Rest all variables same.
So E > F

karu26 · Answer

We can attack this question in a much simple way without the need of any calculation. Given that the investment amount and interest rate are the same, the amount which is being compounded more frequently will accumulate more interest than the amount that is not being compounded at the same rate.
Hence
E>F
Option B is the correct answer.

Elliot and Faye invest $5000 each in different banks

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Elliot and Faye invest $5000 each in different banks

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards